Last Updated on July 24, 2020 Probability density is the relationship between observations and their probability. Some outcomes of a random variable will have low probability density and other outcomes will have a high probability density. The overall shape of the probability density is referred to as a probability distribution, and the calculation of probabilities for specific outcomes of a random variable is performed by a probability density function, or PDF for short. It is useful to know the probability […]

Last Updated on May 6, 2020 Probability quantifies the uncertainty of the outcomes of a random variable. It is relatively easy to understand and compute the probability for a single variable. Nevertheless, in machine learning, we often have many random variables that interact in often complex and unknown ways. There are specific techniques that can be used to quantify the probability for multiple random variables, such as the joint, marginal, and conditional probability. These techniques provide the basis for a […]

Last Updated on December 6, 2019 Probability for a single random variable is straight forward, although it can become complicated when considering two or more variables. With just two variables, we may be interested in the probability of two simultaneous events, called joint probability: the probability of one event given the occurrence of another event called the conditional probability, or just the probability of an event regardless of other variables, called the marginal probability. These types of probability are easy […]

Last Updated on November 1, 2019 Probability calculations are frustratingly unintuitive. Our brains are too eager to take shortcuts and get the wrong answer, instead of thinking through a problem and calculating the probability correctly. To make this issue obvious and aid in developing intuition, it can be useful to work through classical problems from applied probability. These problems, such as the birthday problem, boy or girl problem, and the Monty Hall problem trick us with the incorrect intuitive answer […]

Last Updated on January 10, 2020 Probability for Machine Learning Crash Course.Get on top of the probability used in machine learning in 7 days. Probability is a field of mathematics that is universally agreed to be the bedrock for machine learning. Although probability is a large field with many esoteric theories and findings, the nuts and bolts, tools and notations taken from the field are required for machine learning practitioners. With a solid foundation of what probability is, it is […]

Last Updated on December 4, 2019 Bayes Theorem provides a principled way for calculating a conditional probability. It is a deceptively simple calculation, although it can be used to easily calculate the conditional probability of events where intuition often fails. Although it is a powerful tool in the field of probability, Bayes Theorem is also widely used in the field of machine learning. Including its use in a probability framework for fitting a model to a training dataset, referred to […]

Last Updated on January 10, 2020 Classification is a predictive modeling problem that involves assigning a label to a given input data sample. The problem of classification predictive modeling can be framed as calculating the conditional probability of a class label given a data sample. Bayes Theorem provides a principled way for calculating this conditional probability, although in practice requires an enormous number of samples (very large-sized dataset) and is computationally expensive. Instead, the calculation of Bayes Theorem can be […]

Last Updated on August 22, 2020 In this tutorial, you will discover how to implement the Bayesian Optimization algorithm for complex optimization problems. Global optimization is a challenging problem of finding an input that results in the minimum or maximum cost of a given objective function. Typically, the form of the objective function is complex and intractable to analyze and is often non-convex, nonlinear, high dimension, noisy, and computationally expensive to evaluate. Bayesian Optimization provides a principled technique based on […]

Probabilistic models can define relationships between variables and be used to calculate probabilities. For example, fully conditional models may require an enormous amount of data to cover all possible cases, and probabilities may be intractable to calculate in practice. Simplifying assumptions such as the conditional independence of all random variables can be effective, such as in the case of Naive Bayes, although it is a drastically simplifying step. An alternative is to develop a model that preserves known conditional dependence […]

Last Updated on July 13, 2020 Information theory is a subfield of mathematics concerned with transmitting data across a noisy channel. A cornerstone of information theory is the idea of quantifying how much information there is in a message. More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated using probability. Calculating information and entropy is a useful tool in machine learning and is used as the basis […]